Boundary Layer Flow past a Stretching Cylinder and Heat Transfer with Variable Thermal Conductivity

ABSTRACT

The boundary layer flow of viscous incompressible fluid over a stretching cylinder has been considered to study flow field and temperature field. Due to non-linearity, a numerical approach called Keller-box technique has been used to compute the values of velocity function f and temperature field at different points of dynamic region. The expressions for skin friction and Nusselt number have also been obtained. The dependence of velocity profile and temperature profile on the dimensionless parameter of practical interest has been analyzed in detail by graphs. The dependence of Skin friction and Nusselt number has been seen through tables.

The boundary layer flow of viscous incompressible fluid over a stretching cylinder has been considered to study flow field and temperature field. Due to non-linearity, a numerical approach called Keller-box technique has been used to compute the values of velocity function f and temperature field at different points of dynamic region. The expressions for skin friction and Nusselt number have also been obtained. The dependence of velocity profile and temperature profile on the dimensionless parameter of practical interest has been analyzed in detail by graphs. The dependence of Skin friction and Nusselt number has been seen through tables.

Cite this paper

R. Rangi and N. Ahmad, "Boundary Layer Flow past a Stretching Cylinder and Heat Transfer with Variable Thermal Conductivity,"*Applied Mathematics*, Vol. 3 No. 3, 2012, pp. 205-209. doi: 10.4236/am.2012.33032.

R. Rangi and N. Ahmad, "Boundary Layer Flow past a Stretching Cylinder and Heat Transfer with Variable Thermal Conductivity,"

References

[1] B. C. Sakiadis, “Boundary-Layer Behaviour on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, 1961, pp. 26-28. doi:10.1002/aic.690070108

[2] L. J. Crane, “Flow past a Stretching Plate,” Zeitschrift für Angewandte Mathematik und Physik, Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695

[3] F. M. White, “Viscous Fluid Flow,” Mc Graw Hill, New York, 2006.

[4] J. E. Daskalakis, “Free Convection Effects in the Boundary Layer along a Vertically Stretching Flat Surface,” Canadian Journal of Physics, Vol. 70, 1993, pp. 1253-1260. doi:10.1139/p92-204

[5] C. H. Chen, “Laminar Mixed Convection Adjacent to Vertical, Continuously Stretching Sheets,” Heat Mass Transfer, Vol. 33, No. 5-6, 1998, pp. 471-476. doi:10.1007/s002310050217

[6] C. H. Chen, “Mixed Convection Cooling of a Heated, Continuously Stretching Surface,” Heat Mass Transfer, Vol. 36, No. 1, 2000, pp. 79-86. doi:10.1007/s002310050367

[7] C. R. Lin and C. K. Chen, “Exact Solution of Heat Transfer from a Stretching Surface with Variable Heat Flux,” Heat Mass Transfer, Vol. 33, 1998, pp. 477-480. doi:10.1007/s002310050218

[8] M. E. Ali, “The Buoyancy Effect on the Boundary Layers Induced by Continuous Surfaces Stretched with Rapidly Decreasing Velocities,” Heat Mass Transfer, Vol. 40, No. 3-4, 2004, pp. 285-291. doi:10.1007/s00231-002-0405-9

[9] M. K. Partha, P. V. S. N. Murthy and G. P. Rajasekhar, “Effect of Viscous Dissipation on the Mixed Convection Heat Transfer from an Exponentially Stretching Surface,” Heat Mass Transfer, Vol. 41, No. 4, 2005, pp. 360-366. doi:10.1007/s00231-004-0552-2

[10] A. Ishak, R. Nazar and I. Pop, “Mixed Convection on a Stagnation Point Flow toward a Vertical, Continuously Stretching Sheet,” Journal of Heat Transfer, Vol. 129, No. 9, 2007, pp. 1087-1090. doi:10.1115/1.2737482

[11] A. Ishak, R. Nazar and I. pop, “Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet,” Heat Mass Transfer, Vol. 44, No. 8, 2008, pp. 921-927. doi:10.1007/s00231-007-0322-z

[12] H. T. Lin and Y. P. Shih, “Laminar Boundary Layer Heat Transfer along Static and Moving Cylinder,” Journal of the Chinese Institute of Engineers, Vol. 3, No. 1, 1980, pp. 73-79. doi:10.1080/02533839.1980.9676650

[13] H. T. Lin and Y. P. Shih, “Buoyancy Effects on the Laminar Boundary Layer Heat Transfer along Vertically Moving Cylinders,” Journal of the Chinese Institute of Engineers, Vol. 4, No. 1, 1981, pp. 47-51. doi:10.1080/02533839.1981.9676667

[14] T. Cebeci and P. Bradshaw, “Physical and Computational Aspects of Convective Heat Transfer,” Springer-Verlag, New-York, 1984.

[15] T. Mahmood and J. H. Merkin, “Similarity Solutions in Axisymmetric Mixed-Convection Boundary-Layer Flow,” Journal of Engineering Mathematics, Vol. 22, No. 1, 1988, pp. 73-92. doi:10.1007/BF00044366

[16] A. Ishak, “Mixed Convection Boundary Layer Flow over a Vertical Cylinder with Prescribed Surface Heat Flux,” Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 19, 2009, pp. 1-8. doi:10.1088/1751-8113/42/19/195501

[1] B. C. Sakiadis, “Boundary-Layer Behaviour on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, 1961, pp. 26-28. doi:10.1002/aic.690070108

[2] L. J. Crane, “Flow past a Stretching Plate,” Zeitschrift für Angewandte Mathematik und Physik, Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695

[3] F. M. White, “Viscous Fluid Flow,” Mc Graw Hill, New York, 2006.

[4] J. E. Daskalakis, “Free Convection Effects in the Boundary Layer along a Vertically Stretching Flat Surface,” Canadian Journal of Physics, Vol. 70, 1993, pp. 1253-1260. doi:10.1139/p92-204

[5] C. H. Chen, “Laminar Mixed Convection Adjacent to Vertical, Continuously Stretching Sheets,” Heat Mass Transfer, Vol. 33, No. 5-6, 1998, pp. 471-476. doi:10.1007/s002310050217

[6] C. H. Chen, “Mixed Convection Cooling of a Heated, Continuously Stretching Surface,” Heat Mass Transfer, Vol. 36, No. 1, 2000, pp. 79-86. doi:10.1007/s002310050367

[7] C. R. Lin and C. K. Chen, “Exact Solution of Heat Transfer from a Stretching Surface with Variable Heat Flux,” Heat Mass Transfer, Vol. 33, 1998, pp. 477-480. doi:10.1007/s002310050218

[8] M. E. Ali, “The Buoyancy Effect on the Boundary Layers Induced by Continuous Surfaces Stretched with Rapidly Decreasing Velocities,” Heat Mass Transfer, Vol. 40, No. 3-4, 2004, pp. 285-291. doi:10.1007/s00231-002-0405-9

[9] M. K. Partha, P. V. S. N. Murthy and G. P. Rajasekhar, “Effect of Viscous Dissipation on the Mixed Convection Heat Transfer from an Exponentially Stretching Surface,” Heat Mass Transfer, Vol. 41, No. 4, 2005, pp. 360-366. doi:10.1007/s00231-004-0552-2

[10] A. Ishak, R. Nazar and I. Pop, “Mixed Convection on a Stagnation Point Flow toward a Vertical, Continuously Stretching Sheet,” Journal of Heat Transfer, Vol. 129, No. 9, 2007, pp. 1087-1090. doi:10.1115/1.2737482

[11] A. Ishak, R. Nazar and I. pop, “Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet,” Heat Mass Transfer, Vol. 44, No. 8, 2008, pp. 921-927. doi:10.1007/s00231-007-0322-z

[12] H. T. Lin and Y. P. Shih, “Laminar Boundary Layer Heat Transfer along Static and Moving Cylinder,” Journal of the Chinese Institute of Engineers, Vol. 3, No. 1, 1980, pp. 73-79. doi:10.1080/02533839.1980.9676650

[13] H. T. Lin and Y. P. Shih, “Buoyancy Effects on the Laminar Boundary Layer Heat Transfer along Vertically Moving Cylinders,” Journal of the Chinese Institute of Engineers, Vol. 4, No. 1, 1981, pp. 47-51. doi:10.1080/02533839.1981.9676667

[14] T. Cebeci and P. Bradshaw, “Physical and Computational Aspects of Convective Heat Transfer,” Springer-Verlag, New-York, 1984.

[15] T. Mahmood and J. H. Merkin, “Similarity Solutions in Axisymmetric Mixed-Convection Boundary-Layer Flow,” Journal of Engineering Mathematics, Vol. 22, No. 1, 1988, pp. 73-92. doi:10.1007/BF00044366

[16] A. Ishak, “Mixed Convection Boundary Layer Flow over a Vertical Cylinder with Prescribed Surface Heat Flux,” Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 19, 2009, pp. 1-8. doi:10.1088/1751-8113/42/19/195501